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= B * A B & A & B & B & A & A < B * A ! & n A = n " 0 & & ! ℵ 0 3) ) 5 [0, 1] " & ) ) & ' ! c ( A ∼ [0, 1] A = c * B & B 1 & B > B 1 B * A B & ! & n m & A & B & ! m n ' + ! (: - A B & α β , A & B & ! & B A β α + β α "" 2 ℵ 0 = c. "" + A α A 2 α , A 2 α > α. ' f : X → Y * a, b ∈ X " ! f (a) = f(b) ϕ ' a ∈ X ! f (a) = f(a) ( a ∼ a ϕ 3 5 f (a) = f(b) f (b) = f(a) ! ϕ ! * f (a) = f(b) f (b) = f(c) f (a) = f(c) ' ϕ \ ϕ Z − & ' & Z & N ! - f : Z → N, f (n) = ⎧ ⎨ ⎩ 2n + 1, agar n ≥ 0 −2n, agar n < 0. f \ & [a, b] [c, d] & " ' a < b, c < d ' & ϕ : [a, b] → [c, d], ϕ(x) = d − c b − a (x − a) + c. ϕ (a) = c, ϕ(b) = d ϕ %%#" ! [0, 1] (0, 1) ' & = "' A = [0, 1], A 1 = (0, 1), B = (0, 1) B 1 = [1/4, 1/2] ``" A ∼ B 1 A 1 = B ! I : A 1 → B, Ix = x ( B ∼ A 1 = "' A ∼ B $ = & \ = & E = [0, 1] , K 1 = (3 −1 , 2 · 3 −1 ) ! & & F 1 = F 1 K 21 = (9 −1 , 2 · 9 −1 ) K 22 = (7·9 −1 , 8·9 −1 ) ! K 2 & & ( F 1 \K 2 = 0, 1 9 2 9 , 1 3 2 3 , 7 9 8 9 , 1 & F 2 3`#"! 5 ' ` 3 −3 ! d K 31 ∪K 32 ∪K 33 ∪K 34 = 1 27 , 2 27 7 27 , 8 27 19 27 , 20 27 25 27 , 26 27 & K 3 F 2 \K 3 F 3 3`#"! 5 ' + ! & & ! F n " * K = ∞ n =1 F n K & & , [0, 1] " K 1 , K 2 , . . . , K n , . . . ! + K & ) $"# [ K & 3 5 Z [0, 1] ! 0, 1, 1 3 , 2 3 , 1 9 , 2 9 , 7 9 , 8 9 , · · · (3.1) K ' K & [0, 1] K ! " ' ! [0, 1] x ! - x = a 1 3 + a 2 3 2 + a 3 3 3 + . . . + a n 3 n + . . . a n > # % . ( 1 3 = 1 3 + 0 3 2 + · · · + 0 3 n + · · · = 0 3 + 2 3 2 + · · · + 2 3 n + · · · [ K & ! ; Z 1 3 , 2 3 ! a 1 # 1 9 , 2 9 7 9 , 8 9 " ! a 2 # 1 27 , 2 27 , 7 27 , 8 27 , 19 27 , 20 27 25 27 , 26 27 ! ! " a 3 # 2 x ∈ [0, 1]\K ! ! " ! a 1 , a 2 , . . . a n , . . . # * " ! - K & " ! ! x ∈ [0, 1] a 1 , a 2 , . . . a n , . . . " # ! " 2 x ∈ K ! a 1 , a 2 , . . . a n , . . . (3.2) " a n 0 2 ' " & & ' ! ! 3`%5 " b 1 , b 2 , . . . , b n , . . . (3.3) " a n = 0 b n = 0 a n = 2 b n = 1 3``5 " [0, 1] x 2 K & [0, 1] ' K & ! () * +, * *+- + # - % M & ϕ M : + ! & f : X → Y X " : + ' `8" & P : R 2 → R, P (x, y) = x R 2 : + . 2 S : R 3 → R + , S (x 1 , x 2 , x 3 ) = x 2 1 + x 2 2 + x 2 3 R 3 : + / * x y ϕ ' ' & & : + ' + ! * α β & ϕ ' c [ & '! + & & Z & $ 2 & & ! " % d & &" & d & \ & &" ' ! & & . R (0, 1) & / ! & & . ! & c * ! A B & " 2 ! A B & A B & $ {x ∈ R : sin x = 0, 5} & % {x ∈ R : cos x ∈ Q} & & & '! ^ & & " ' * ξ ^ & ξ * & " . * A & B B & C A & C / 1 & : " [0 Download 1.57 Mb. Do'stlaringiz bilan baham: 
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